Problem: Solve for $x$ and $y$ using elimination. ${2x+2y = 38}$ ${-3x+2y = -12}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${2x+2y = 38}$ $3x-2y = 12$ Add the top and bottom equations together. $5x = 50$ $\dfrac{5x}{{5}} = \dfrac{50}{{5}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {2x+2y = 38}\thinspace$ to find $y$ ${2}{(10)}{ + 2y = 38}$ $20+2y = 38$ $20{-20} + 2y = 38{-20}$ $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ You can also plug ${x = 10}$ into $\thinspace {-3x+2y = -12}\thinspace$ and get the same answer for $y$ : ${-3}{(10)}{ + 2y = -12}$ ${y = 9}$